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marshall27 [118]
4 years ago
8

Consider the following hypotheses: H0: mean = 5 H1: mean < 5 A test is performed with a sample of size 25. The sample mean wa

s 4.73 and the population standard deviation is 1.2. Assume that the population is approximately normal. Use the TI-84 PLUS calculator to compute the P-value. Round your answer to four decimal places (for example: 0.0138). Write only a number as your answer.
Mathematics
1 answer:
kondor19780726 [428]4 years ago
7 0

Answer:

0.1406.

Step-by-step explanation:

Given : H_o:\mu = 5

           H_1:\mu < 5  

To Find : compute the P-value.

Solution:

Sample size = 25

n < 30

So, we will go for t-test

Now we are given that  the population standard deviation is 1.2.

\sqrt{\frac{s}{n}}=1.2 Where s is the variance

\sqrt{\frac{s}{25}}=1.2

\sqrt{s}=6

s = 6^2

s = 36

So, the variance is 36

we require sample standard deviation for t test

So, Sample standard deviation = \sqrt{\frac{s}{n-1}}

                                                  = \sqrt{\frac{36}{25-1}}

                                                  = 1.2247

Formula of t-test = \frac{m-\mu}{\frac{s}{\sqrt{n}}}

Where s is the standard deviation of sample

Sample mean = 4.73

Mean = \mu = 5

s = 1.2247

n =25

So,  t=\frac{5-4.73}{\frac{1.2247}{\sqrt{25}}}

t=1.1023

So, p value with respect to t-table is 0.1406.

Hence p-value is  0.1406.

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